Date: October 2, 2024

Assignment

Create a web page presentation using R Markdown that features a plot created with Plotly. Host your webpage on either GitHub Pages, RPubs, or NeoCities. Your webpage must contain the date that you created the document, and it must contain a plot created with Plotly. We would love to see you show off your creativity.

The data set under consideration and goal

Consider the pre-loaded data set “EuStockMarkets” consisting of daily closing prices of major European stock indices, 1991-1998. The markets of interest are DAX, SMI, CAC, and FTSE. We wish to determine a linear model for DAX given SMI, CAC, and FTSE as covariates.

data(EuStockMarkets)
EuStockMarkets <- as.data.frame(EuStockMarkets)
head(EuStockMarkets)
##       DAX    SMI    CAC   FTSE
## 1 1628.75 1678.1 1772.8 2443.6
## 2 1613.63 1688.5 1750.5 2460.2
## 3 1606.51 1678.6 1718.0 2448.2
## 4 1621.04 1684.1 1708.1 2470.4
## 5 1618.16 1686.6 1723.1 2484.7
## 6 1610.61 1671.6 1714.3 2466.8

Model selection

By the following nested likelihood ratio test, FTSE is not a significant covariate.

fit1 <- lm(DAX ~ 1, data = EuStockMarkets)
fit2 <- update(fit1, DAX ~ 1+SMI)
fit3 <- update(fit2, DAX ~ 1+SMI+CAC)
fit4 <- update(fit3, DAX ~ 1+SMI+CAC+FTSE)
anova(fit1,fit2,fit3,fit4)
## Analysis of Variance Table
## 
## Model 1: DAX ~ 1
## Model 2: DAX ~ SMI
## Model 3: DAX ~ SMI + CAC
## Model 4: DAX ~ SMI + CAC + FTSE
##   Res.Df        RSS Df  Sum of Sq          F Pr(>F)    
## 1   1859 2187625263                                    
## 2   1858   38532840  1 2149092423 179597.275 <2e-16 ***
## 3   1857   22217334  1   16315505   1363.469 <2e-16 ***
## 4   1856   22209221  1       8113      0.678 0.4104    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Therefore we predict DAX with SMI and CAC.

fit_no_int <- lm(DAX ~ SMI + CAC, data=EuStockMarkets)
summary(fit_no_int)
## 
## Call:
## lm(formula = DAX ~ SMI + CAC, data = EuStockMarkets)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -336.83  -79.21   10.15   82.37  326.60 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.102e+02  1.617e+01  -13.01   <2e-16 ***
## SMI          4.808e-01  4.741e-03  101.42   <2e-16 ***
## CAC          5.017e-01  1.359e-02   36.93   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 109.4 on 1857 degrees of freedom
## Multiple R-squared:  0.9898, Adjusted R-squared:  0.9898 
## F-statistic: 9.05e+04 on 2 and 1857 DF,  p-value: < 2.2e-16

Plots

library(plotly)
plot_ly(EuStockMarkets, x = ~SMI, y = ~CAC, z = ~DAX)
plot_ly(EuStockMarkets, x = ~SMI, y = ~CAC, color = ~DAX)